On Jan 23, 2008 4:08 PM, Jonathan Bober <[EMAIL PROTECTED]> wrote:
>
> I just realized a source of my confusion. The docstring that I quoted
> was not actually wrong in the way that I thought is was, but was
> apparently deceptive (to me). Perhaps some people are already aware of
> this, but GF(5)
I just realized a source of my confusion. The docstring that I quoted
was not actually wrong in the way that I thought is was, but was
apparently deceptive (to me). Perhaps some people are already aware of
this, but GF(5), GF(25), and GF(5^100) are all different types, and so
have different docstr
Hi All,
Just a few comments: there are three possible concepts for
generator[s]:
1) As a field over its prime field or base field (function gen(),
category Field or Algebra);
2) As a vector space over its base field (function
additive_generators(), category Module)
3) As a group, restricted to t
Sorry, I was confused. You and William are right.
Martin
--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: [EMAIL PROTECTED]
--~--~-~--~~~---~--~~
To post to this g
On Jan 23, 2008 4:06 AM, Martin Albrecht <[EMAIL PROTECTED]> wrote:
>
> > > By contrast F.multiplicative_gen() does make sense for all finite
> > > fields so should be provided, though not necessarily computed until
> > > requested for the reasons given by Martin. (It seems that with the
> > > cu
On 23/01/2008, Martin Albrecht <[EMAIL PROTECTED]> wrote:
>
> > > By contrast F.multiplicative_gen() does make sense for all finite
> > > fields so should be provided, though not necessarily computed until
> > > requested for the reasons given by Martin. (It seems that with the
> > > current impl
> > By contrast F.multiplicative_gen() does make sense for all finite
> > fields so should be provided, though not necessarily computed until
> > requested for the reasons given by Martin. (It seems that with the
> > current implementation of non-prime fiinite fields this comes for
> > free, but
Thanks for taking the time to read and respond to my lengthy
contribution. I agree with everything you say!
Sorry to those who don't like the more mathematical discussions on
sage-devel -- personally I find them more interesting than the
notebook interface! but one of Sage's strengths is surely
On Jan 22, 2008 3:46 AM, John Cremona <[EMAIL PROTECTED]> wrote:
>
> Thoughts on this thread:
>
> For finite fields (or any other fields) the concept of additive
> generator makes no sense -- only finite prime fields have one and it
> is hardly a useful concept then since every nonzero element is
Thoughts on this thread:
For finite fields (or any other fields) the concept of additive
generator makes no sense -- only finite prime fields have one and it
is hardly a useful concept then since every nonzero element is one.
It's different if talking about generators (plural!) which I think is
w
> In this case, the docstring needs to be corrected, because the statement
> that "All elements x of self are expressed as log_{self.gen()}(p)
> internally" is not true, right? (Extrapolating from this sentence and my
> two examples led me to make my previous statements.) Probably it is true
> tha
Ok, I was wrong. I'm convinced that sage has the correct behavior, which
I think is:
GF(q).gen() returns an element x of GF(q) such that the smallest
subfield of GF(q) containing x is GF(q).
In this case, the docstring needs to be corrected, because the statement
that "All elements x of self are
Hi,
It is probably a bias of the choice of (additive) generators for
finite field
extensions which results in the primitive field element also being a
generator for the multiplicative group (confusingly called a
"primitive
element of the finite field").
It is not possible to set GF(q).gen() to a
On Jan 20, 2008 10:54 PM, Jonathan Bober <[EMAIL PROTECTED]> wrote:
>
> I don't like the behavior illustrated below. Briefly, my problem is that
> GF(p).gen() gives a generator for the additive group of GF(5), while
> GF(p^n).gen() gives a generator for for multiplicative group of GF(p^n)
> (n > 1
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